2/6b+5=20-b

Solution for 2/6b+5=20-b equation:

2/6b+5=20-b

We move all terms to the left:

2/6b+5-(20-b)=0


Domain of the equation: 6b!=0

b!=0/6

b!=0

b∈R


We add all the numbers together, and all the variables

2/6b-(-1b+20)+5=0

We get rid of parentheses

2/6b+1b-20+5=0

We multiply all the terms by the denominator


1b*6b-20*6b+5*6b+2=0

Wy multiply elements

6b^2-120b+30b+2=0

We add all the numbers together, and all the variables

6b^2-90b+2=0

a = 6; b = -90; c = +2;
Δ = b2-4ac
Δ = -902-4·6·2
Δ = 8052
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8052}=\sqrt{4*2013}=\sqrt{4}*\sqrt{2013}=2\sqrt{2013}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2013}}{2*6}=\frac{90-2\sqrt{2013}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2013}}{2*6}=\frac{90+2\sqrt{2013}}{12}
$